What are some datasets to train an MLP on simple tasks?
There are a ton of sample datasets our there you can play with. A bunch of good ones install with R in the datasets package.  Luckily you can download them independently if you're not an R user.  Try  https://vincentarelbundock.github.io/Rdatasets/datasets.html

You might also be interested in the MNIST database which is one of the canonical databases used in handwriting recognition research.

Beyond that, you can look at / ask on http://datasets.reddit.com and/or http://opendata.reddit.com and you'll find all sorts of useful datasets.

And finally, don't overlook the UCI Machine Learning Repository.